The present inventor has already accomplished an invention relating to a swiveling faucet and filed Japanese Patent Application No. 96625/1971 and U.S. Pat. No. 3,834,665. The faucet of the invention includes a water outlet tube which is swivelable to open and close the water passage and a valve disk comprising a first member 10 and a second member 20 as shown in FIG. 1. The outlet tube is provided, at its base end, with a cylindrical member having a semicircular curved surface. When turned, the cylindrical member depresses the second member, with the laterally horizontal projecting portion of its curved surface in contact therewith, to close the valve or relieves the second member of the pressure to open the valve. According to the invention, the second member must be formed with a semicircular recessed surface 20a adapted for full face-to-face contact with the semicircular curved surface of the cylindrical member and opposite side guide channels 20b to render the second member movable up and down. The guide channels 20b are therefore defined by thin wall portions. This construction involves the problem that when the laterally horizontal portion depresses the second member, the thin wall portions become distorted and interfere with projecting guide pieces formed on the inside of the valve casing and extending axially thereof to guide the second member, consequently hampering smooth valve opening and closing operation. In addition to the guide pieces, the valve casing further has stoppers disposed at an upper interior portion thereof and spaced apart from each other by a distance to permit the cylindrical member to turn through an angle of 180.degree.. Thus the construction has another problem in that these guide pieces and stoppers impede insertion of the second member into the casing, making it difficult to smoothly place the second member thereinto. Furthermore because the valve disk is adapted to restrict the pressure of water only with the elasticity of the first member, the packing or the first member may possibly be damaged when subjected to an excessive depressing force, this leading to leakage of water. These are problems experienced with the valve of the type described.